In a large mixing bowl, combine eggs, carrots, vanilla extract, and oil. Whisk very well until completely combined.
Sift in flour, sugar, baking soda, baking powder, cinnamon, and nutmeg. Whisk well and pour into the prepared baking pan. Set aside.
With electric mixer, beat cream cheese until smooth. Add sugar and beat for a couple of minutes.
Add egg and beat until combined.
Add sour cream and heavy cream and beat until smooth. Scrape sides and bottom of the bowl and beat for a couple more minutes.
Add cinnamon, nutmeg, and flour. Beat until combined.
Drop spoonfuls of cheesecake batter all over the carrot cake batter. Using a small spatula (or a butter knife), gently swirl cheesecake batter into carrot cake batter. Make sure that batter is even throughout the pan so it bakes evenly. If not, you can gently shake the pan to even it out.
Bake for 43-45 minutes.
To make the glaze, add powder sugar sugar and cinnamon to a small bowl. Add warmed heavy cream and whisk until all smooth. Place glaze into a piping bag. Cut off a small tip off the piping bag when ready to glaze the cake and drizzle the cake with cinnamon glaze.